Question

A sphere of surface area \( 4 \, \text{m}^2 \), temperature 400 K, emissivity 0.5 is in an environment of 200 K. The net rate of energy exchange is (take \( \sigma = 5.67 \times 10^{-8} \, \text{Wm}^{-2} \text{K}^{-4} \))

• A. 3260.8 W
• B. 1632.4 W
• C. 2721.6 W
• D. 4216.4 W

Hint:

Use \( P = \epsilon \sigma A (T^4 - T_0^4) \) for radiative energy exchange problems.

Answer 1

The Correct Option is C

Use Stefan-Boltzmann law:
\[ P = \epsilon \sigma A (T^4 - T_0^4) = 0.5 \cdot 5.67 \times 10^{-8} \cdot 4 \cdot (400^4 - 200^4) \] \[ = 2 \cdot 5.67 \times 10^{-8} \cdot (2.56 \times 10^9 - 1.6 \times 10^8) = 2 \cdot 5.67 \times 10^{-8} \cdot 2.4 \times 10^9 \approx 2721.6 \, \text{W} \]